I have been programming in a "learn-by-doing" fashion for almost 2 years now and I consider myself fairly good however, I really wish to build a good foundation of Computer Science/Computer Engineering and most people recommend I start off with SICP. (Structure and Interpretation of Computer Programs)
I wished to know
A personal experience: Like you I am trying to learn programming by self-study and I started off with SICP. As I am a ancient historian and archaeologist, I have no background in maths, engineering or real computer science (just good knowlegde in stuff like LaTeX, HTML and CSS). My last lessons in math are now 15 years ago. Although I am working through SICP with a math book at my side the explanations given in SICP are really sufficient to understand the stuff. I really appreciate SICP, it is demanding, but great fun. I also would recommend to buy it as a book, I prefer that from reading on screen.
Sometimes you have to cope with some difficulties because language standards have changed (eg. Running SICP Pattern Matching Rule Based Substitution Code) or the authors assume existing functions which are just defined later in the book (eg. How do I get the functions put and get in SICP, Scheme, Exercise 2.78 and on). As a you always will find solutions or hints on the web this is nothing which should bother you.